I think I can understand how you're feeling right now. I gave birth in Dec'07 and was a new mommy - really green-horn as I didn't even know how to carry my baby! Needless to say breastfeeding was a flop and I'd to gripple with that on top of not being able to soothe my baby when he fussed or turned cranky.
I finally managed to soothe him when he was about 1 month as mother in law showed me how to carry him using her way just before she returned M'sia. However my happiness was shortlived. I stayed at my mum's when my son was 1-3MO and during this time he preferred my mum whenever he fussed, at milktime or nap/bedtime.
Yes, I felt so lost and a complete failure then. I always had that typical impression that a baby would always want their mother. I guess my experience told me this is not often true....sometimes for some unknown reasons, the baby prefers someone else.
My son is now 10MO and I survived...so can you! I know it's not easy to overcome the negative emotions but you've to hang in there. Baby will grow up and their needs will change with each stage. Maybe you can't handle this stage so well but that doesn't mean you can't handle the later stages. With time you'll also improve your motherhood skills to better cope with baby.
dont't be too hard on yourself...it's ok if someone else can handle your baby better, and if they do and are willing to help, let them. Give yourself a deserved break at such times especially if you're the main caregiver. You can always bond with your baby when he's not fussy or cranky and play with him at such times. If you can, dont't give up breastfeeding since you're able to do it and your baby didn't reject you at such times. This is also a good bonding time between you and baby.
Try to chat with a friend or your hubby about how you feel so that your worries are heard and you can lighten up your mood. It helps if you dont't feel so stressed up when handling your baby. If your depression doesn't go away after some time or gets worse, you may want to consider seeing a doctor in case post-natal blues.
Ganbette! Jia You! dont't give up on yourself or your baby ...you both need time to adapt to each other.